Example 4

Let A be a commutative local ring and $B = A[[X_i]]_{i\in I}$ an algebra of formal power series with coefficients in A (III, §2, No. 11, p. 456). By Proposition 6 of IV, §4, No. 4, p. 30, the ring B is local, and its maximal ideal consists of the formal power series with constant term in the maximal ideal of A. In particular, if A is a field, the maximal ideal of $A[[X_i]]_{i\in I}$ consists of the formal power series with constant term zero.